Functions of completely regular growth

✍ Scribed by Ronkin, L. I

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Leaves: 404
• Series: Mathematics and Its Applications (Soviet Series) 81
• Category: Library

✦ Synopsis

This monograph deals with functions of completely regular growth (FCRG), i.e., functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of on variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications -- functions having a bounded spectrum and finite exponential sums. For research mathematicians and physicists whose work involves complex analysis and its applications. The book will also be useful to those working in some areas of radiophysics and optics. Read more...

Abstract: This monograph deals with functions of completely regular growth (FCRG), i.e., functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of on variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications -- functions having a bounded spectrum and finite exponential sums. For research mathematicians and physicists whose work involves complex analysis and its applications. The book will also be useful to those working in some areas of radiophysics and optics

✦ Table of Contents

Front Matter....Pages i-xii
Entire Functions of Completely Regular Growth of One Variable....Pages 1-40
Subharmonic Functions of Completely Regular Growth in ℝ n ....Pages 41-100
Entire Functions of Completely Regular Growth in ℂ n ....Pages 101-140
Functions of Completely Regular Growth in the Half-Plane or a Cone....Pages 141-243
Functions of Exponential Type and Bounded on the Real Space ( Fourier Transforms of Distribution of Compact Support )....Pages 244-289
Quasipolynomials....Pages 290-345
Mappings....Pages 346-379
Back Matter....Pages 381-392

✦ Subjects

Functions of a Complex Variable; Potential Theory; Several Complex Variables and Analytic Spaces; Applications of Mathematics